Philosophy and Memory Traces defends two theories of autobiographical memory. One is a bewildering historical view of memories as dynamic patterns in fleeting animal spirits, nervous fluids which rummaged through the pores of brain and body. The other is new connectionism, in which memories are 'stored' only superpositionally, and reconstructed rather than reproduced. Both models, argues John Sutton, depart from static archival metaphors by employing distributed representation, which brings interference and confusion between memory traces. Both raise urgent issues about control (...) of the personal past, and about relations between self and body. Sutton demonstrates the role of bizarre body fluids in moral physiology, as philosophers from Descartes and Locke to Coleridge struggled to control their own innards and impose cognitive discipline on 'the phantasmal chaos of association'. Going on to defend connectionism against Fodor and critics of passive mental representations, he shows how problems of the self are implicated in cognitive science. (shrink)

This essay examines one of the cornerstones of Leibniz's defense of teleology within the order of nature. The first section explores Leibniz's contributions to the study of geometrical optics, and argues that his "Most Determined Path Principle" or "MDPP" allows him to bring to the fore philosophical issues concerning the legitimacy of teleological explanations by addressing two technical objections raised by Cartesians to non-mechanistic derivations of the laws of optics. The second section argues that, by drawing on laws such as (...) the MDPP, Leibniz is able to introduce a thin notion of teleology that gives him the resources to respond to the most pressing charges of his day against teleological explanations within natural philosophy. Finally, the third section argues that contemporary philosophers have been overly hasty in their dismissal of Leibniz's account of natural teleology, and indeed that their own generally thin conceptions of teleology have left them with few well-motivated resources for resisting his elegant position. (shrink)

This paper argues that Spinoza's notions of “conatus” and “power of acting” are derived by means of generalization from the notions of “force of motion” and “force of determination” that Spinoza discussed in his Principles of Cartesian Philosophy to account for interactions among bodies on the basis of their degrees of contrariety. I argue that in the Ethics, Spinoza's ontology entails that interactions must always be accounted for in terms of degrees of “agreement or disagreement in nature” among interacting things. (...) The notion of “power of acting” is used to express the extent to which a thing's conatus is aided or restrained by external causes on the basis of its degree of agreement or disagreement in nature with them. “Power of acting” generalizes the same approach and method of resolution at the basis of the notion of “force of determination” in order to account for causal interactions not only among the simplest bodies but also among more complex individuals. (shrink)

I consider a somewhat obscure but important feature of Descartes’s physics that concerns the notion of the “force of rest.” Contrary to a prominent occasionalist interpretation of Descartes’s physics, I argue that Descartes himself attributes real forces to resting bodies. I also take his account of rest to conflict with the view that God conserves the world by “re-creating” it anew at each moment. I turn next to the role of rest in Malebranche. Malebranche takes Descartes to endorse his own (...) occasionalist version of physics. However, he nonetheless rejects Descartes’s account of rest by appealing to the fact that whereas God’s production of motion requires a power beyond the mere power to create, his production of rest requires only the latter power. It turns out that this argument in Malebranche is incompatible with the sort of “re-creationist” account of divine conservation that he is widely thought to have inherited from Descartes. (shrink)

Introduction Conatus is a specific concept within Descartes’s physics. In particular, it assumes a crucial importance in the purely mechanistic description of the nature of light – an issue that Des- cartes considered one of the most crucial challenges, and major achievements, of his natural phil- osophy. According to Descartes’s cosmology, the universe – understood as a material continuum in which there is no vacuum – is composed of a number of separate yet interconnected vortices. Each of these vortices consists (...) in a set of bands rotating around their centres. The bands are com- posed of corpuscles of the three elements, each distinguished on the basis of their different shapes and sizes. The small globules of the second element, although impeded by the other parts of heaven, strive to move away from the centre of the vortex around which they revolve, thus exerting a certain force against the surrounding bodies. This striving or conatus, though a mere force rather than a genuine motion, is transmitted instan- taneously and along straight lines from body to body. According to Descartes, then, the nature of light consists in this striving alone. This account must be understood as strictly connected to the fundamental laws that regulate the Cartesian world. It is particularly important to recall that for Descartes the centrifugal force exerted by a rotating body is understood to be a consequence of the intrinsic rectilinearity of every motion. As the second of the three Laws of Nature set forth in Book II of the Principles of Philosophy establishes, “all motion is in itself rectilinear; and hence any body moving in a circle tends to move away from the centre of the circle which it describes as proved by the fact that a stone rotating in a sling tends to move centrifugally along the tangent of each point described by a circle.1 Similarly, each of the globules of the second element “strives to recede with a great force from the centre of the vortex in which it rotates; it is in fact prevented by the other globules placed all around, not differently than a stone in a sling”. Within this framework, as I show later, conatus occurs when a body’s intrinsic tendency to rectilinear motion is impeded by an external constraint. As Stephen Gaukroger notes, the use of the term conatus in the Principles – like “vis” and “ action ” – shows that Descartes “cannot avoid dynamic terminology”, despite his declared intent “to construe motion in a purely kinematic way”. Indeed, Gaukroger observes that the notions of force action and striving are systematically employed in the Principles – appearing 290, 59 and 8 times, respectively. Also noteworthy, conatus was – together with the more familiar concepts of actio and vis – a significant element of the conceptual apparatus of Scholastic natural philosophy. As will be seen later – and this is the first goal of this paper – here the concept of conatus had a very specific function. Indeed, it was a central part of the Aristotelian- Scholastic account of gravitation. Conatus was used to refer to the striving of a body to move towards its natural place – especially in cases where its natural motion was hindered or impeded by an external mover. This specific use of the concept of conatus can be found in texts on natural philosophy from the end of the sixteenth through the late seventeenth century. Notably, it occurs in some of the late -Scho- lastic texts which held special significance for Descartes’s thought. Therefore, Descartes introduces conatus in a context in which this concept already had a very specific meaning, and one of which he was very probably aware. The possible relations between these two apparently very different con- cepts have therefore to be scrutinized. I thereby propose to undertake a comparison between the Scho- lastic and the Cartesian conceptions of conatus. I hope to show that certain traits of the former are indeed echoed by the latter, although adapted to the much changed physical paradigm of Cartesian physics. In fact, Descartes’s conatus, though sharing some important similarities with the old one, underwent significant transformations in terms of both its meaning and its application. However, I hope to show that these concepts are both used to describe the behaviour of bodies in relation to their intrinsic motive tendency, and in particular when this tendency is impeded or prevented. Such a reconstruction offers two main areas of interest. On an immediate level, it furthers the general efforts of scholars over the past decades to reconstruct the full extent of the relations between Descartes’s thought and Scholastic philosophy. However, there is another significant reason for taking an interest in the ties between the Scholastic and the Cartesian conceptions of conatus. Indeed, the Cartesian conatus must be seen as crucial to a proper understanding of the broader, diverse conceptualization that this idea enjoyed in the thought of many of the most important philosophers of the early modern period, namely Spinoza, Hobbes and Leibniz. In particular, Spinoza, were directly influenced by Descartes in their unique formulations of conatus. Thus a reconstruction of the context in which Descartes formulated his conatus and of its relations to a pre-existing Scholastic conception will enable us to better reconstruct the history of this idea in the early modern period. The paper is structured as follows: in the first part, I provide a thorough review of the Scho- lastic employment of the concept conatus – both its meaning and the extent of its usage. I then show that it occurs in some of the most prominent Cartesian sources. Finally, I shall provide an account of Descartes’s theory of circular motion and conatus with the specific aim of empha- sizing the elements of both continuity and discontinuity that justify the claim that Descartes’s con- ception of conatus is reminiscent of the Scholastic one. (shrink)

This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the (...) field, it lays down a much-needed marker of progress to date and provides a platform for informed and coherent future analysis and research of the subject. -/- The publication comes at a time of heightened worldwide concern over the standard of science and mathematics education, attended by fierce debate over how best to reform curricula and enliven student engagement in the subjects There is a growing recognition among educators and policy makers that the learning of science must dovetail with learning about science; this handbook is uniquely positioned as a locus for the discussion. -/- The handbook features sections on pedagogical, theoretical, national, and biographical research, setting the literature of each tradition in its historical context. Each chapter engages in an assessment of the strengths and weakness of the research addressed, and suggests potentially fruitful avenues of future research. A key element of the handbook’s broader analytical framework is its identification and examination of unnoticed philosophical assumptions in science and mathematics research. It reminds readers at a crucial juncture that there has been a long and rich tradition of historical and philosophical engagements with science and mathematics teaching, and that lessons can be learnt from these engagements for the resolution of current theoretical, curricular and pedagogical questions that face teachers and administrators. (shrink)

Argues that Descartes's commitment to mind-body causation leads to a commitment to body-body causation.

Spinoza’s conatus doctrine, the main proposition of which claims, “[e]ach thing, to the extent it is in itself, strives [conatur] to persevere in its being” (E3p6), has been the subject of growing interest. This is understandable, for Spinoza’s psychology and ethics are based on this doctrine. In my paper I shall examine the way Spinoza argues for E3p6 in its demonstration which runs as follows: "For singular things are modes by which God’s attributes are expressed in a certain and determinate (...) way (by 1p25c), i.e. (by 1p34), things that express, in a certain and determinate way, God’s power, by which God is and acts. And no thing has anything in itself by which it can be destroyed, or which takes its existence away (by p4). On the contrary, it is opposed to everything which can take its existence away (by p5). Therefore, to the extent it can, and is in itself, it strives to persevere in its being." This argument has been severely criticized for being defective in many ways. E3p6d contains four items, E1p25c, 1p34, 3p4, and 3p5. Most often, only the two last mentioned are regarded as doing any real work in the demonstration. However, I shall argue that having a proper grasp of Spinoza’s concept of power enables us see that the demonstration’s beginning, built on E1p25c and 1p34, brings forth a certain dynamic framework in which finite things are centers of causal power, capable of producing effects in virtue of their essences. My examination of this framework shows the beginning of the demonstration to be irreplaceable: in the end, conatus is one form of power, and E1p25c and 1p34 not only bring the notion of power into play, but also inform us on how finite things’ power should be understood in the monistic system. So, I disagree with such commentators as Jonathan Bennett, Edwin Curley, Daniel Garber, Michael Della Rocca, and Richard Manning, who see Spinoza as trying to derive the conatus doctrine from E3p4 and 3p5 alone; and I agree with Alexandre Matheron, Henry Allison, and Martin Lin, who stress the importance of E1p25c and 1p34. -/- However, this still leaves us the task of reconstructing the whole derivation and showing how its various ingredients fit together. If E1p25c and 1p34 are so important, could E3p6 not be derived from them alone, as Martin Lin has argued? In other words, why are E3p4 and 3p5 needed at all? To answer these questions I shall provide an interpretation of E3p6d that explains how the argument is supposed to work. E1p25c and 1p34 say that finite things are, in essence, dynamic causers, which, in case of opposition, truly resist opposing factors with their power and do not simply cease their causal activities whenever facing obstacles; in other words, they strive against any opposition. However, this is not enough to guarantee that they could not act self-destructively or restrain their own power, which would make them incapable of self-preservation. But this would go against E3p4, “No thing can be destroyed except through an external cause,” and Spinoza uses it to claim, “no thing has anything in itself by which it can be destroyed, or which takes its existence away.” So all this allows Spinoza to hold that finite things are consistent causers, that is, entities endowed with power and, insofar they cause effects solely in virtue of their essence, they never use their power self-destructively. The significance and role of the final item in the demonstration, E3p5 (“Things are of a contrary nature, i.e., cannot be in the same subject, insofar as one can destroy the other”), still needs to be determined. Indeed, considering its content and the way it is used in the demonstration, it seems to be a surprisingly decisive ingredient in the argument. Namely, what “each thing, to the extent it is in itself,” that is, insofar as any thing is considered disregarding everything external to it, strives to preserve, is its being (esse), not simply its present state. This together with E3p5’s view of subjecthood – which I shall explicate in my paper – suggests that we should rethink what kind of “being” or “existence” is meant in E3p6. Indeed, for Spinoza, each subject has a definable essence from which, as far as the subject in question is in itself, certain properties or effects necessarily follow; consequently a subject’s full being involves not only instantiating a certain essence, but also those properties inferable from the essence-expressing definition. Thus, E3p5 is meant to bring forward that things are not merely non-self-destroyers but subjects from whose definitions properties follow; and as Spinoza thinks to have shown (by E1p25c and 1p34) that finite modifications are entities endowed with power, any subject has true power to produce the properties or effects derivable from its definition, which, Spinoza claims, implies opposing everything harmful. In other words, things exercise power as their definition states, i.e. according to their definitions, and thus bringing in the idea of things as expressers of power enables Spinoza to convert logical oppositions (of E3p5) into real ones (of E3p6). To summarize, Spinoza reasons that each true finite thing is, in itself, an expresser of power (E1p25c, 1p34) that never acts self-destructively (E3p4) but instead strives to drive itself through opponents to produce effects as they follow from the definition of the thing in question (E1p25c, 1p34, and 3p5). Therefore, “each thing, to the extent it is in itself, strives to persevere in its being.” The demonstration of E3p6 has its roots deep in Spinoza’s ontology, and since its concept of power is supposed to provide the metaphysical grounding for real opposition, the importance of E1p25c and 1p34 should not be underestimated just because Spinoza – as often happens – puts his point exceedingly briefly. Moreover, the derivation is basically valid and contains no superfluous elements. Finally, all this tells us something decisive about the meaning of Spinoza’s doctrine: according to it, things are active causers whose “power to exist and act” has conatus character in temporality, amounting not only to striving to prolong the duration of one’s actualization but also to striving to be as active or autonomous as possible, that is, to attain a state determined by the striving subject’s essence alone. (shrink)

ArgumentThis paper discusses the theory of motion of the philosopher Honoré Fabri (1608–1688), a senior representative of early modern Jesuit scientists. It argues that the consensus prevailing among historians – according to which Fabri's theory of impetus is diametrically opposed to Galileo's or Descartes' concept of inertia – is false. It shows: that Fabri carefully constructed his concept of impetus in order to easily incorporate the principle of linear conservation of motion (designated here as “limited inertia”), by adopting formal (rather (...) than efficient) causality between impetus and motion and by allowing impetus to act only along straight lines; that he explicitly deemed Aristotle's famous “inertial paradox” not as a paradox at all; and that linear conservation of motion was not limited to “counterfactual” circumstances but played a significant part in his discrete theory of free fall and constituted an integral component of his general physical (and even mathematical) philosophy. However, the paper also shows that Fabri's notion of inertia was restricted to one dimension only, and therefore should indeed be considered “limited.” In his analysis of horizontal projectiles, Fabri explicitly rejected Galileo's important principle of superposition, and thus revealed significant constraints to his “inertial” thinking. (shrink)

Descartes' account of the material world relies heavily on time. Most importantly, time is a component of speed, which figures in his fundamental conservation principle and laws. However, in his most systematic discussion of the concept, time is treated as some-how reducible both to thought and to motion. Such reductionistic views, while common among Descartes' late scholastic contemporaries, are very ill-suited to Cartesian physics. I show that, in spite of the apparent identifications with thought and motion, Cartesian time retains—in the (...) form of what I will call 'successive duration'—precisely the intrinsic structure necessary to serve as an independent parameter of quantitative physics. As is often the case with Descartes, he gives the impression of embracing traditional doctrines while in fact radically transforming the underlying concepts to serve his scientific agenda. His theory of time, though formulated in Aristotelian terms, anticipates Newton in important respects. (shrink)

How does Newton approach the challenge of mechanizing gravity and, more broadly, natural philosophy? By adopting the simple machine tradition’s mathematical approach to a system’s co-varying parameters of change, he retains natural philosophy’s traditional goal while specifying it in a novel way as the search for impressed forces. He accordingly understands the physical world as a divinely created machine possessing intrinsically mathematical features, and mathematical methods as capable of identifying its real features. The gravitational force’s physical cause remains an outstanding (...) problem, however, as evidenced by Newton’s onetime reference to active principles as the “genuine principles of the mechanical philosophy”. (shrink)

Although Newton carefully eschews questions about gravity’s causal basis in the published Principia, the original version of his masterwork’s third book contains some intriguing causal language. “These forces,” he writes, “arise from the universal nature of matter.” Such remarks seem to assert knowledge of gravity’s cause, even that matter is capable of robust and distant action. Some commentators defend that interpretation of the text—a text whose proper interpretation is important since Newton’s reasons for suppressing it strongly suggest that he continued (...) to endorse its ideas. This article argues that the surface appearance of Newton’s causal language is deceptive. What does New- ton intend with his causal language if not a full causal hypothesis? His remarks actually indicate a way of considering the force mathematically, something he contrasts to the structure of the force as it really is in nature. In explaining that, he identifies a significant disjunction between the physical force itself and mathematical ways of considering it, and the text’s significance lies in its view of the force’s structure and in the questions raised about the relationship between mathematical representations and the physical world. (shrink)

This paper compares Newton’s and Descartes’s conceptions of the complex relationship between physics and metaphysics.

One of the chief concerns of the young Descartes was with what he, and others, termed “physico-mathematics”. This signalled a questioning of the Scholastic Aristotelian view of the mixed mathematical sciences as subordinate to natural philosophy, non explanatory, and merely instrumental. Somehow, the mixed mathematical disciplines were now to become intimately related to natural philosophical issues of matter and cause. That is, they were to become more ’physicalised’, more closely intertwined with natural philosophising, regardless of which species of natural philosophy (...) one advocated. A curious, short-lived yet portentous epistemological conceit lay at the core of Descartes’ physico-mathematics—the belief that solid geometrical results in the mixed mathematical sciences literally offered windows into the realm of natural philosophical causation—that in such cases one could literally “see the causes”. Optics took pride of place within Descartes’ physico-mathematics project, because he believed it offered unique possibilities for the successful vision of causes. This paper traces Descartes’ early physico-mathematical program in optics, its origins, pitfalls and its successes, which were crucial in providing Descartes resources for his later work in systematic natural philosophy. It explores how Descartes exploited his discovery of the law of refraction of light—an achievement well within the bounds of traditional mixed mathematical optics—in order to derive—in the manner of physico-mathematics—causal knowledge about light, and indeed insight about the principles of a “dynamics” that would provide the laws of corpuscular motion and tendency to motion in his natural philosophical system. (shrink)

In the Principles of Philosophy, Descartes attempts to explicate the well-known phenomena of varying bodily size through an appeal to the concept of "solidity," a notion that roughly corresponds to our present-day concept of density. Descartes' interest in these issues can be partially traced to the need to define clearly the role of matter in his natural laws, a problem particularly acute for the application of his conservation principle. Specifically, since Descartes insists that a body's "quantity of motion," defined as (...) the product of its "size" and speed, is conserved in all material interactions, it is imperative that he explain how solidity influences the magnitude of this force. As a means of resolving this problem, Descartes postulated an idealized condition of "perfect solidity" which correlates a body's "agitation" force (a forerunner of Newton's concept of non-accelerating, or "inertial" motion) with the interplay of its volume, surface area, and composition of minute particles. This essay explores this often misunderstood aspect of Descartes' physics, as well as the special function of idealized conditions in his collision rules. Contrary to those commentators who regard "perfect solidity" as a stipulation on bodily impact, this notion, it will be argued, is primarily concerned with the internal composition of macroscopic bodies, and only indirectly with their collision characteristics. Along the way, many of Descartes' hypotheses will be shown to display a level of sophistication and intricacy that, despite their essential incompatibility, belie several of the common misconceptions of Cartesian science. (shrink)

The rich connections between metaphysics and natural philosophy in the early modern period have been widely acknowledged and productively mined, thanks in no small part to the work of Margaret Wilson, whose book, Descartes, served as an inspirational example for a generation of scholars. The task of this paper is to investigate one particular such connection, namely, the relation between occasionalist metaphysics and strict mechanism. My focus will be on the work of Nicholas Malebranche, the most influential Cartesian philosopher after (...) Descartes himself. I begin with two crucial facts about Malebranche’s philosophy: (1) Malebranche was an occasionalist, that is, he held that God was the only true cause, that all modifications of bodies and of minds can be produced by God alone. (2) Malebranche adhered firmly to strict mechanism. By strict mechanism, I mean the view, found most prominently in Descartes and in Boyle’s more ideological writings, that the qualities of bodies are exhausted by a very short list (size, shape, motion, and perhaps solidity) and that, most importantly, bodies interact only at contact by impact. Another way of describing this “contact action” requirement is as the thesis that the only fundamental laws of physics are laws of inertial motion and laws of the communication of motion at impact. In.. (shrink)

There does not seem to be a consistent way to ground the concept of “force” in Cartesian first principles. In this article, I first review the literature on the subject. Then, I offer an alternative interpretation of force—one that seems to be coherent and consistent with Descartes’ project. Not only does the new position avoid the problems of previous interpretations, but it does so in such a way as to support and justify those previous interpretations. *Received June 2007; revised June (...) 2009. †To contact the author, please write to: Department of Philosophy, University of Washington, Box 353350, Seattle, WA 98195; e‐mail: [email protected]. (shrink)

This paper examines Descartes' problematic relational theory of motion, especially when viewed within the context of his dynamics, the Cartesian natural laws. The work of various commentators on Cartesian motion is also surveyed, with particular emphasis placed upon the recent important texts of Garber and Des Chene. In contrast to the methodology of most previous interpretations, however, this essay employs a modern "spacetime" approach to the problem. By this means, the role of dynamics in Descartes' theory, which has often been (...) neglected in favor of kinematic factors, is shown to be central to finding a solution to the puzzle of Cartesian motion. (shrink)

I argue that Descartes' Second Causal Proof of God in the Third Meditation evidences, and commits him to, the belief that time is "strongly discontinuous" -- that is, that there is actually a gap between each consecutive moment of time. Much of my article attempts to reconcile this interpretation, the "received view," with Descartes' statements about time, space, and matter in his other writings, including his correspondence with various philosophers.

: This paper presents a detailed account of Descartes' derivation of his second law of nature—the law of rectilinear motion—from a priori metaphysical principles. Unlike the other laws the proof of the second depends essentially on a metaphysical assumption about the temporal immediacy of God's operation. Recent commentators (e.g., Des Chene and Garber) have not adequately explained the precise role of this assumption in the proof and Descartes' reasoning has continued to seem somewhat arbitrary as a result. My account better (...) reveals the dependence of the second law on fundamental principles about time and causality. (shrink)

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be (...) also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators on it. One can interpret special Minkowski space involved by special relativity and the qubit Hilbert space of quantum information as Fourier counterparts immediately noticing that general relativity means gravitation as the Fourier counterpart of non-Hermitian operators implying non-unitarity and the violation of energy conservation and thus destroying Pauli’s particle paradigm. Since the Standard model obeys it, this explains the impossibility of “quantum gravitation” in any framework conservatively generalizing the Standard model so that it would include gravitation along with electromagnetic, weak, and strong interactions. Einstein’s geometrization of gravitation can be continued into a purely mathematical theory of it following Euclid’s realization for geometry to be exhaustively built in a deductive and axiomatic way as well as Riemann’s parametrization of all the class of Euclidean and non-Euclidean geometries by “space curvature”, then being generalized to Minkowski space as the operators on pseudo-Riemannian space as the Einstein field equation means gravitation. The transition from mathematical gravitation to logical one can rely on the historical lesson of the pair of Lobachevski’s and Riemann’s approaches now “reversely”, i.e., from the latter to the former. Logical gravitation is linkable to Hegel’s dialectical logic and ontological dialectics abandoning their interpretations as a new zero logic substituting classical propionyl logic. The approach of ontomathematics generalizing that of ontology, traceable even to Aristotle’s reformation of Plato’s doctrine, needs Hegel’s doctrine to be formalized as a first-order logic naturally containing Boolean algebra, isomorphic to both classical propositional logic and set theory being the class of all first-order logics, as a sub-logic along with Peano arithmetic as another sub-logic. The first-order logic at issue is called Hilbert arithmetic and elaborated in detail in other papers. It allows for both self-foundation of mathematics to be internally proved as complete and furthermore, quantum mechanics reinterpreted as quantum information to be included by the qubit Hilbert space interpretable in turn as a dual and physical counterpart of Hilbert arithmetic in a narrow sense, that is, both counterparts constitute Hilbert arithmetic in a wide sense, being mathematical and physical simultaneously and thus overcoming the Cartesian dualism of “body” gapped from “mind” by an abyss. Then, the proper philosophical interpretation of gravitation to be the fundamental ontomathematical force or interaction overcomes the ridiculous belief of the Big Bang wrongly alleged to be a scientific theory. Ontomathematical gravitation suggests an omnipresent and omnitemporal medium of “God’s” creation “ex nihilo” following only the natural necessity of quantum-information conservation particularly and locally manifested as energy conservation. (shrink)

Descartes’s most extensive discussion of the law of refraction and the shape of the anaclastic lens is contained in Rule 8 of "Rules for the Direction of the Mind". Few reconstructions of Descartes’s discovery of the law of refraction take Rule 8 as their basis. In Rule 8, Descartes denies that the law of refraction can be discovered by purely mathematical means, and he requires that the law of refraction be deduced from physical principles about natural power or force, the (...) nature of the action of light, and the behavior of light rays in a variety of transparent media. For over a century, however, there has been broad agreement that Descartes discovered the law of refraction by purely mathematical means, and that he only later provided the relevant physical rationale (via comparisons or analogies) in Dioptrics II. I execute each step in Descartes’s proposed deduction of the law of refraction and the shape of the anaclastic lens in Rule 8 and concretely show how Descartes could have discovered the law of refraction and the shape of the anaclastic by its means. Rule 8, I argue, reflects Descartes’s actual path to the discovery of the law of refraction and the shape of the anaclastic lens. (shrink)

This paper aims both to tackle the technical issue of deciphering Hobbes’s derivation of the sine law of refraction and to throw some light to the broader issue of Hobbes’s mechanical philosophy. I start by recapitulating the polemics between Hobbes and Descartes concerning Descartes’ optics. I argue that, first, Hobbes’s criticisms do expose certain shortcomings of Descartes’ optics which presupposes a twofold distinction between real motion and inclination to motion, and between motion itself and determination of motion; second, Hobbes’s optical (...) theory presented in Tractatus Opticus I constitutes a more economical alternative, which eliminates the twofold distinction and only admits actual local motion, and Hobbes’s derivation of the sine law presented therein, which I call “the early model” and which was retained in Tractatus Opticus II and First Draught, is mathematically consistent and physically meaningful. These two points give Hobbes’s early optics some theoretical advantage over that of Descartes. However, an issue that has baffled commentators is that, in De Corpore Hobbes’s derivation of the sine law seems to be completely different from that presented in his earlier works, furthermore, it does not make any intuitive sense. I argue that the derivation of the sine law in De Corpore does make sense mathematically if we read it as a simplification of the early model, and Hobbes has already hinted toward it in the last proposition of Tractatus Opticus I. But now the question becomes, why does Hobbes take himself to be entitled to present this simplified, seemingly question-begging form without having presented all the previous results? My conjecture is that the switch from the early model to the late model is symptomatic of Hobbes’s changing views on the relation between physics and mathematics. (shrink)

It is common to assume that Descartes did not have a conception of an object's matter density independently of its size, but this is a rather incomplete assessment of the early modern natural philosopher's theory. Key to our understanding of Descartes's physics is a consideration of the ratios between the quantities of the different types of matter in which an object consists. As these ratios determine the degree of an object's porosity and elasticity, they also affect in Descartes's theory the (...) phenomena of gravity and weight. (shrink)

In this paper I want to examine in some detail one eighteenth-century attempt to restructure the foundations of mechanics, that of Leonhard Euler. It is now generally recognized that the idea, due to Mach, that all that happened in the eighteenth century was the elaboration of a deductive and mathematical mechanics on the basis of Newton's Laws is misleading at best. Newton's Principia needed much more than a reformulation in analytic terms if it was to provide the basis for the (...) comprehensive mechanics that was developed in the eighteenth century. Book II of the Principia, in particular, where the problem of the resistance offered to the motion of a finite body by a fluid medium was raised, was generally thought to be in large part mistaken and confused. There were also a number of areas crucial to the unification of mechanics which Newton did not deal with at all in the Principia: particularly the dynamics of rigid, flexible and elastic bodies, and the dynamics of several bodies with mutual interactions. Although a start had been made on some of these topics in the seventeenth century , it was only in the eighteenth century that they were subjected to detailed examination, and Euler's contribution to the development of these topics, and hence to the unification of mechanics, was immense. (shrink)

: This paper focuses on Princess Elisabeth of Bohemia's philosophical views as exhibited in her early correspondence with René Descartes. Elisabeth's criticisms of Descartes's interactionism as well as her solution to the problem of mind-body interaction are examined in detail. The aim here is to develop a richer picture of Elisabeth as a philosophical thinker and to dispel the myth that she is simply a Cartesian muse.

: In this paper I address the vexed question of secondary causation in René Descartes' physics, and examine several influential interpretations, especially the one recently proposed by Dennis Des Chene. I argue that interpreters who regard Cartesian bodies as real secondary causes, on the grounds that the modes of body include real forces, contradict Descartes' account of modes. On the other hand, those who deny that Descartes affirms secondary causation, on the grounds that forces cannot be modes of extension, commit (...) Descartes to the problematic view that the undetermined and immutable will of God is the sole cause of determinate and variable motions. Des Chene's contextualist approach to Descartes' texts leads him to an intermediate position that combines elements of both interpretations. However, in my view, Des Chene's interpretation likewise fails to resolve apparent tensions in Descartes' claims. I thus propose to separate the issue of secondary causation from what Des Chene dubs 'the problem of force'. On the basis of this approach, and a study of Jesuit commentaries familiar to Descartes, I develop a new interpretation which takes seriously Descartes' claim that the laws of nature are the secondary and particular causes of particular motions and changes in motion. (shrink)

Descartes is usually taken to be a strict reductionist, and he frequently describes his work in reductionist terms. This dissertation, however, makes the case that he is a nonreductionist in certain areas of his philosophy and natural philosophy. This might seem like simple inconsistency, or a mismatch between Descartes's ambitions and his achievements. I argue that here it is more than that: nonreductionism is compatible with his wider commitments, and allowing for irreducibles increases the explanatory power of his system. Moreover, (...) Descartes depends on nonreductionist knowledge and on irreducibles in order to maintain his epistemology and metaphysics. That is, there is more in the Cartesian world than mind, matter, and God. (shrink)

[The title in English: "The Concept of Life in Spinoza's Philosophy."] Tarkastelen tässä kirjoituksessa elämän käsitteen merkitystä Spinozan filosofian eri vaiheissa, ja selvitän, miksi käsitteellä ei enää hänen Etiikkansa ontologiassa ole keskeistä asemaa. Samalla piirtyy esiin joitakin Spinozan ajattelun olennaisia aspekteja.

Este artigo explora a relação que Descartes estabelece com as noções de forma e de matéria do aristotelismo escolástico ao tratar da interação entre as substâncias nas correspondências com Elisabeth, Gassendi e Arnauld. Partindo do exemplo do peso utilizado por Descartes em diversas cartas, traça-se uma relação de identidade entre a noção de forma em Tomás de Aquino e de pensamento em Descartes, assim como se traça a crítica à noção de forma, entendida como qualidade oculta, para os corpos inanimados. (...) Por fim, explora-se a interpretação ocasionalista do sistema cartesiano e a relevância dos movimentos celestes para a explicação dos movimentos naturais em Tomás de Aquino.This paper deals with the relation that Descartes points between his system and concepts of matter and form from Aristotelian scholasticism. The resemblance arises when Descartes treats interaction among substances in correspondences with Elisabeth, Gassendi and Arnauld. Beginning with the example of the scholastic concept of weight, used many times by Descartes, this article traces an identity between concepts of form in Thomas Aquinas and of thought in Descartes, as well as traces his criticism on the concept of form, understood as hidden qualities, to inanimate bodies. Finally, this paper investigates Cartesian occasionalism as well as the importance of celestial movements for a better comprehension of nature in Thomas Aquinas. (shrink)

The Oxford Handbook of the History of Physics brings together cutting-edge writing by more than twenty leading authorities on the history of physics from the seventeenth century to the present day. By presenting a wide diversity of studies in a single volume, it provides authoritative introductions to scholarly contributions that have tended to be dispersed in journals and books not easily accessible to the general reader. While the core thread remains the theories and experimental practices of physics, the Handbook contains (...) chapters on other dimensions that have their place in any rounded history. These include the role of lecturing and textbooks in the communication of knowledge, the contribution of instrument-makers and instrument-making companies in providing for the needs of both research and lecture demonstrations, and the growing importance of the many interfaces between academic physics, industry, and the military. (shrink)

Essay review of Daniel Garber, 1992, Descartes' Metaphysical Physics, University of Chicago Press, Chicago and London, xiv + 389 pp., and Michael Friedman,: 1992, Kant and the Exact Sciences, Harvard University Press, Cambridge, Mass., and London, xvii + 357 pp. These two books display the historical connection between science and philosophy in the writings of Descartes and Kant. They show the place of science in, or the scientific context of, these authors' central metaphysical doctrines, pertaining to substance and its properties, (...) the metaphysics of force and causal agency, the relation of geometry to matter and to space, and the structure of cognition. In so doing, they provide an image of philosophy as an intellectually and culturally engaged enterprise, an image according to which it makes little sense to make pronouncements about the foundations of knowledge or the possibilities for science without direct engagement with the living practice of scientific and other cognitive enterprises. However, in some areas they did not engage the context as fully as needed; their interpretations of particular arguments and indeed of whole philosophical programs suffered thereby. (shrink)